Sentence examples for regularity issue from inspiring English sources

The global regularity issue has been thoroughly investigated for the 3D micropolar fluid equations and many important regularity criteria have been established (see [13 19]).

end{aligned} (5.3)Note that there is a regularity issue here, since (varphi ) is convex, hence T is defined only a.e. and it is just a BV map.

We also notice that if the partial derivatives of the viscosity and resistivity are zero, the global regularity issue has been established in [19].

One main focus of recent research on the 2D Boussinesq equations has been on the global regularity issue when only fractional dissipation is present.

The global regularity issue has been thoroughly investigated for the 3D Navier-Stokes equations and many important regularity criteria have been established (see [7 16] and the references therein).

Moreover, He and Xin [23, 24] showed that the velocity field u plays a dominant role in the regularity issue and derived a criterion in terms of the velocity field u alone (see also [25, 26] for the Besov spaces cases).

Yang, Jiu and Wu [42] examined the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal diffusion, and further established the global well-posedness for the 2D Boussinesq equations with a new range of fractional powers of the Laplacian.

And yet with imperious regularity, Vatican officials issue their relished condemnations.

It's a square dance that happens with regularity around this issue.

However, the issue of regularity and uniqueness of such a given weak solution remains a challenging open problem.

Our next goal is to illustrate the issue of regularity of a model by providing a simple, albeit admittedly artificial, example of a model, which is not regular.